How to make convnets aware what the image actually is, not what is depicted on it?
You seem to be wanting some description of the 'style' of an image. 

To make that work in general, I'd guess that would actually require quite a lot of pre-processing to present 'texture elements' (rather than pixels) as the basic features. 

This is quite speculative, but one approach might be to use Iterated Function Systems as a means of extracting these.

Whether 'spatial adjacency' (and hence CNN) is then the best approach to make higher-level decisions about these elements is (AFAIK) a matter for experiment.